Explanation Given information : The function f ( x ) = x + 2 sin x distance from point Formulaused : The slope ( m ) of tangent line to the curve y = f ( x ) is given by m = d y d x Calculations: The given function is y = f ( x ) = x + 2 sin x . The slope of tangent to the graph of the function y = f ( x ) is m = d d x ( x + 2 sin x ) = 1 + 2 cos x The tangent line to the curve will be horizontal (or parallel to x -axis) when m =0 , i.e., 1 + 2 cos x = 0 ⇒ cos x = − 1 2

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 3.3, Problem 59E

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Tofind:The values of x for which the graph of the given function have a horizontal tangent.

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Chapter 3.3, Problem 58E

Chapter 3.3, Problem 60E

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Chapter 3 Solutions

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Tofind: The values of x for which the graph of the given function have a horizontal tangent.

Solution Summary: The author calculates the slope of tangent line to the graph of the given function y=f(x)=x+2mathrmsinx.

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Tofind:The values of x for which the graph of the given function have a horizontal tangent.

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